sin〔π-α〕-cos〔π+α〕=√2/3sinα+cosα=√2/3(sinα>cosα)(sinα+cosα)^2=2/91+2sinαcosα=2/92sinαcosα=-7/9(sinα-cosα)^2=1-2sinαcosα=1+7/9=16/9sinα-cosα=±4/3所以sinα-cosα=4/3